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A164091
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Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
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3
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1, 41, 1640, 65600, 2624000, 104960000, 4198399180, 167935934400, 6717436064820, 268697390145600, 10747893507936000, 429915656401920000, 17196622899456671580, 687864781713487950000, 27514585897949409744420
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OFFSET
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0,2
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COMMENTS
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The initial terms coincide with those of A170760, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
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LINKS
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FORMULA
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G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(780*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).
G.f.: (1+x)*(1-x^6)/(1 -40*x +819*x^6 -780*x^7). - G. C. Greubel, Apr 25 2019
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MATHEMATICA
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CoefficientList[Series[(1+x)*(1-x^6)/(1-40*x+819*x^6-780*x^7), {x, 0, 20}], x] (* G. C. Greubel, Apr 25 2019 *)
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PROG
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(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-40*x+819*x^6-780*x^7)) \\ G. C. Greubel, Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-40*x+819*x^6-780*x^7) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^6)/(1-40*x+819*x^6-780*x^7)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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